Description
A first stage in the study of polymer solution science ended with the worldwide acceptance of the concept of the excluded-volume effect in the mid 1950s shortly after the publication of the celebrated book by Flory [1] in 1953. In the next stage, activity was centered mainly in the study of dilute solution behavior of flexible polymers within the Flory framework which consists of that concept for the Gaussian chain and the universality of its state without that effect. The theoretical developments were then made by an application of orthodox but rather classical techniques in statistical mechanics for many-body problems with a more rigorous consideration of chain connectivity, thus all leading except for a few cases to the so-called two-parameter (TP) theory, which predicts that all dilute solution properties may be expressed in terms of the unperturbed () dimension of the chain and its total effective excluded volume. The results derived until the late 1960s are summarized in Yamakawa’s 1971 book [2] along with a comparison with experimental data. In the meantime, on the other hand, an experimental determination of the (asymptotic) unperturbed chain dimension for a wide variety of long flexible polymers [3] brought about great advances in its theoretical evaluation for arbitrary chain length on the basis of the rotational isomeric state (RIS) model [4], and all related properties are sophisticatedly treated in Flory’s second (1969) book [5].
Subsequently, the advances in the field have been diversified in many directions. The foremost of these is a new powerful theoretical approach to the excludedvolume problems by an application of the scaling concepts and renormalization group theory, which began in the early 1970s when the analogy between many-body problems in the Gaussian chain and magnetic systems was discovered [6, 7]. These techniques enable us to derive asymptotic forms for various molecular properties as functions of chain length (or molecular weight) for long enough chains. The basic scaling ideas and their applications to polymer problems are plainly explained by de Gennes [8] in his renowned third book, while the details of the methods and results of the polymer renormalization group theory are described in the review article by Oono [9] and also in the books by Freed [10] and by des Cloizeaux and Jannink [11].
At about the same time there occurred new developments in the dynamics of polymer constrained systems in two directions. One concerns dilute solutions, and the other concentrated solutions and melts. In particular, there have been significant advances in the latter. Although the single-chain dynamics was first formulated by Kirkwood [12] in 1949 for realistic chains with rigid constraints on bond lengths and bond angles, dynamical properties related to global chain motions in dilute solution have long been discussed on the basis of the Gaussian (spring-bead) chain [2, 13– 16]. However, the study of the constrained-chain dynamics was initiated by Fixman and Kovac [17] in 1974 in order to treat local properties, and much progress in actual calculations has been made possible by slight coarse-graining of the conventional bond chain [18, 19] (see below).
In condensed or many-chain systems, on the other hand, intermolecular constraints, that is, entanglement effects play an important role, and the chain motion in such an environment is very difficult to treat by considering intermolecular forces of the ordinary dispersion type. Indeed, this had been for long one of the unsolved problems in polymer science until 1971 when a breakthrough was brought about by de Gennes [8, 20], who introduced the concept of the reptation in a tube, the concept of the tube itself being originally due to Edwards [21]. In their book, Doi and Edwards [22] summarize comprehensively the successful applications of the tube model to viscoelastic properties of concentrated solutions and melts of long flexible polymers.